For an ideal monoatomic gas, an illustration of three different paths A,(B+C) and (D+E) from an initial state `P_(1),V_(1),T_(1)` to a final state `P_(2),V_(2),T_(1)` is shown in the given figure .

Path A represents a reversible isothermal from `P_(1)V_(1)" to "P_(2),V_(2)`, path (B+C) represent a reversible adiabatic expansion (B) from `P_(1),V_(1),T_(1)" to " P_(3),V_(2),T_(2)` followed by reversible heating of the gas at constant volume (C) from `P_(3),V_(2),T_(2) " to " P_(2),V_(2),T_(1)`. Path (D+E) represents a reversible expansion at constant pressure `P_(1)(D)` from `P_(1),V_(1),T_(1) " to "P_(1),V_(2),T_(3)` followed by a reversible cooling at constant volume `V_(2)(E)` form `P_(1),V_(2),T_(3) " to "P_(2),V_(2),T_(1)`
What is `DeltaS` for path (A)?

Options

A. `nr" In"(V_(2))/(V_(1))`
B. `-nr" In"(V_(2))/(V_(1))`
C. zero
D. `nR(V_(2)-V_(1))`

Answer

a